Finite Group Databasebeta

← #22581178

Subgroups — #22581178

Order 8896.

112 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14555775C211yesmaximal, characteristic, complemented
2C2×#14555774C211yesmaximal, characteristic
3#17984831C211yesmaximal, characteristic
4#17984807C211yesmaximal, characteristic, complemented
5Dic139⋊C8C211yesmaximal, characteristic, complemented
6#17984762C211yesmaximal, characteristic
7#103×C139C211yesmaximal, characteristic, complemented
8C2×Dic278C2211yescharacteristic
9C2×D556C2211yescharacteristic
10#14555775—22no—
11#14555774—22no—
12C2×C139⋊C8C2211yescharacteristic
13Dic139⋊C4—21no—
14(C2×D139)⋊C4—21no—
15(C2×D139)⋊C4—21no—
16C4×Dic139—21no—
17C4×Dic139C2211yescharacteristic
18C2×Q8×C139C2211yescharacteristic
19C2×C8×C139C2211yescharacteristic
20C4⋊C4×C139C2211yescharacteristic
21C22×D139—21no—
22Dic278—21no—
23Dic278D412yes—
24D556—21no—
25D556—21no—
26C2×Dic139—21no—
27C2×Dic139D411yescharacteristic
28C2×Dic139D411yescharacteristic
29C139⋊C8—21no—
30Q8×C139—21no—
31Q8×C139—21no—
32C2×C4×C139—21no—
33C2×C4×C139—21no—
34C2×C4×C139C2311yescharacteristic
35C8×C139—21no—
36C22×C139C2×D411yescharacteristic
37C2×D139—41no—
38C2×D139—41no—
39C2×D139—41no—
40C4×C139—41no—
41C4×C139—41no—
42C4×C139C2×D411yescharacteristic
43C4×C139#4111yescharacteristic
44Dic139—22no—
45Dic139—21no—
46Dic139—21no—
47C2×C139#12111yescharacteristic
48C2×C139#13511yescharacteristic
49C2×C139#13711yescharacteristic
50D139—81no—
51C139#46411yescharacteristic, complemented, Sylow
52#464—1391nomaximal, Sylow
53C2×Q16—1391no—
54C2×SD16—1391no—
55#124—1391no—
56C4×Q8—1391no—
57C4⋊C8—1391no—
58#103D13911yescharacteristic, complemented
59#102—1391no—
60C2×Q8—1391no—
61C2×Q8C2×D13911yescharacteristic
62C2×D4—1391no—
63Q16—2782no—
64SD16—2782no—
65C2×C8—1391no—
66C2×C8C2×D13911yescharacteristic
67C4⋊C4—2781no—
68C4⋊C4C2×D13911yescharacteristic
69C22⋊C4—2781no—
70C22⋊C4—2781no—
71C42—2781no—
72C42—1391no—
73C23—2781no—
74Q8—21no—
75Q8—21no—
76Q8—2781no—
77Q8—1392no—
78D4—2781no—
79D4—2781no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—2781no—
83C2×C4—1391no—
84C2×C4—1391no—
85C2×C4C22×D13911yescharacteristic
86C8—21no—
87C8—2781no—
88C22—5561no—
89C22—5561no—
90C22—5561no—
91C22D4×D13911yescharacteristic
92C4—41no—
93C4—41no—
94C4—2782no—
95C4—2781no—
96C4—2781no—
97C4D4×D13911yescharacteristic
98C4#1455578511yescharacteristic
99C2—11121no—
100C2#1798481511yescharacteristic
101C2#1798486311yescharacteristic
102C2#1798487411yescharacteristic
subgroupG/H
centerC22D4×D139
commutatorC2×C4×C139C23
FrattiniC2×C4C22×D139
Fitting#103×C139C2
socleC22×C139C2×D4
hypercenter#103D139
hypocenterC139#464
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14555775C2semidirect
4. #17984807C2semidirect
5. Dic139⋊C8C2semidirect
7. #103×C139C2semidirect
51. C139#464semidirect
58. #103D139semidirect